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In the optically thick radiative diffusion in a star approximation, the heat flux is $\mathbf{F}=-\chi \nabla T$. The conductivity depends on opacity, mass density and temperature. It relates a material temperature gradient to energy transport and must not be confused with the emergent effective temperature.

In uniformly rotating stellar hydrostatic equilibrium, composition-uniform thermodynamic quantities are functions of the total potential. Radiative conductivity gives $\mathbf{F}=f(\varphi )\nabla \varphi$, with $f=-\chi dT/d\varphi$. On one surface, $f$ is constant, so the outward flux is $F_n=fg$. The Stefan–Boltzmann law therefore gives $T_e\propto g^{1/4}$. This is a surface-flux law: the material temperature constant on an interior equipotential is not the latitude-dependent emergent effective temperature.

With proton–proton chain energy generation $ϵ\propto \rho T^4$ and Kramers' opacity law $\kappa \propto \rho T^{-7/2}$, homology relations for radiative stars giveThe Hertzsprung-Russell diagram relation has $d\log L/d\log T_{\mathrm{eff}}=284/69$, with effective temperature increasing toward the left in the usual plotting convention.

A red dwarf is a cool low-mass main-sequence star. The lowest-mass red dwarfs are fully convective.

A red giant is an evolved star with a large radius and low effective temperature. On the first giant branch, a low- or intermediate-mass star is powered primarily by shell hydrogen burning around a helium-rich core.

A star with broadly Sun-like properties; the range depends on the stated classification criterion. In elementary planetary estimates, a solar mass, solar radius, and solar effective temperature are common approximate inputs, rather than consequences of the name alone.

Classification of stellar spectra by features controlled mainly by temperature and also by surface gravity and composition. The O-B-A-F-G-K-M temperature sequence does not mean a corresponding sequence in bulk hydrogen abundance.

Stellar evolution is the change of a star's structure and composition as nuclear reactions, energy transport, mass loss, and interactions proceed.

The bolometric luminosity of a star is its total radiated power integrated over all wavelengths. A band or spectral luminosity instead specifies a restricted spectral range. The Hertzsprung-Russell diagram compares total luminosity with effective temperature.

The physical radius assigned to a star, with a specified surface convention.

The distribution of radiation from a star with wavelength or frequency, including its continuum and absorption lines. Continuum colors and temperature-dependent line strengths provide complementary estimates of effective temperature. Spectra of an unresolved binary star may need to be separated by eclipse observations or their different velocity shifts before the component effective temperatures can be inferred.

A geometrically thin, optically thick disk has a radially varying effective temperature. Relativistic transport and an atmosphere model convert its thermal spectrum into an inferred emitting area and inner radius. Black-hole mass, distance, inclination and spectral hardening are important external constraints. Selecting thermal-state observations with moderate luminosity limits contamination and the breakdown of the thin-disk approximation. Relating the fitted inner radius to the innermost stable circular orbit remains a physical modeling assumption.

The Zanstra method estimates a central star's effective temperature by comparing its observed nonionizing continuum with the absorbed ionizing-photon rate inferred from nebular recombination lines. If ${\Phi }_{E_0}(T)={\int }_{E_0/h}^{\infty }{B}_{\nu }(T)/(h\nu )d\nu$, then $[F_{\ell }/(h{\nu }_{\ell }{F}_{{\nu }_o,\ast })][\beta /{\alpha }_{\ell }^{\mathrm{eff}}]={\Phi }_{E_0}(T_s)/B_{{\nu }_o}(T_s)$ when the line traces the full appropriate ionizing budget. Both the distance and stellar radius cancel. Density inhomogeneity also cancels from the integrated recombination estimate when the coefficient ratio is known; photon leakage, dust and mixed-species transfer can invalidate the simple budget.